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Option type

In programming languages (more so functional programming languages) and type theory, an option type or maybe type is a polymorphic type that represents encapsulation of an optional value; e.g., it is used as the return type of functions which may or may not return a meaningful value when they are applied. It consists of a constructor which either is empty (often named None or Nothing), or which encapsulates the original data type A (often written Just A or Some A).

A distinct, but related concept outside of functional programming, which is popular in object-oriented programming, is called nullable types (often expressed as A?). The core difference between option types and nullable types is that option types support nesting (Maybe (Maybe A)Maybe A), while nullable types do not (String?? = String?).

Option types as monads

The option type is a monad, which means it follows the algebraic laws associated with monads:

The option monad can also be described in terms of functions return, fmap and join, where the latter two are given by:

The option monad is an additive monad: it has Nothing as a zero constructor and the following function as a monadic sum:

The resulting structure is an idempotent monoid.

Names and definitions

In different programming languages, the option type has various names and definitions.

  • In Agda, it is named Maybe with variants nothing and just a.
  • In Coq, it is defined as Inductive option (A:Type) : Type := | Some : A -> option A | None : option A..
  • In Haskell, it is named Maybe, and defined as data Maybe a = Nothing | Just a.
  • In Idris, it is defined as data Maybe a = Nothing | Just a.
  • In OCaml, it is defined as type 'a option = None | Some of 'a.
  • In Rust, it is defined as enum Option<T> { None, Some(T) }.
  • In Scala, it is defined as parameterized abstract class '.. Option[A] = if (x == null) None else Some(x)...
  • In Standard ML, it is defined as datatype 'a option = NONE | SOME of 'a.
  • In Swift, it is defined as enum Optional<T> { case none, some(T) } but is generally written as T?.

In type theory, it may be written as: . This expresses the fact that for a given set of values in , an option types adds exactly on additional value (the empty value) to the set of valid values for .

In languages having tagged unions, as in most functional programming languages, option types can be expressed as the tagged union of a unit type plus the encapsulated type.

In the Curry–Howard correspondence, option types are related to the annihilation law for ∨: x∨1=1.

An option type can also be seen as a collection containing either one or zero elements.

Examples

Scala

Scala implements Option as a parameterized type, so a variable can be an Option, accessed as follows:[1]

// Defining variables that are Options of type Int
val res1: Option[Int] = Some(42)
val res2: Option[Int] = None

// sample 1 :  This function uses pattern matching to deconstruct Options
def compute(opt: Option[Int]) = opt match {
  case None => "No value"
  case Some(x) => "The value is: " + x
}

// sample 2 :  This function uses monad method
def compute(opt: Option[Int]) = opt.fold("No Value")(v => "The value is:" + v )

println(compute(res1))  // The value is: 42
println(compute(res2))  // No value

Two main ways to use an Option value exist. The first, not the best, is the pattern matching, as in the first example. The second, the best practice is a monadic approach, as in the second example. In this way, a program is safe, as it can generate no exception or error (e.g., by trying to obtain the value of an Option variable that is equal to None). Thus, it essentially works as a type-safe alternative to the null value.

OCaml

OCaml implements Option as a parameterized variant type. Options are constructed and deconstructed as follows:

(* Deconstructing options *)
let compute opt = match opt with
  | None -> "No value"
  | Some x -> "The value is: " ^ string_of_int x

print_endline (compute None) (* "No value" *)
print_endline (compute (Some 42)) (* "The value is: 42" *)

F#

(* This function uses pattern matching to deconstruct Options *)
let compute = function
  | None   -> "No value"
  | Some x -> sprintf "The value is: %d" x

printfn "%s" (compute <| Some 42)(* The value is: 42 *)
printfn "%s" (compute None)      (* No value         *)

Haskell

-- This function uses pattern matching to deconstruct Maybes
compute :: Maybe Int -> String
compute Nothing  = "No value"
compute (Just x) = "The value is: " ++ show x

main :: IO ()
main = do
    print $ compute (Just 42) -- The value is: 42
    print $ compute Nothing -- No value

Swift

func compute(_ x: Int?) -> String {
  // This function uses optional binding to deconstruct optionals
  if let y = x {
    // y is now the non-optional `Int` content of `x`, if it has any
    return "The value is: \(y)"
  } else {
    return "No value"
  }
}

print(compute(42)) // The value is: 42
print(compute(nil)) // No value
func compute(_ x: Int?) -> String {
  // This function uses `map` to transform the optional if it has a value,
  // or pass along the nil if it doesn't. If `map` results in nil,
  // the nil coalescing operator `??` sets a fall-back value of "No value"
  return x.map { unwrappedX in "The value is: \(unwrappedX)" } ?? "No value"
}

print(compute(42)) // The value is: 42
print(compute(nil)) // No value
func compute(_ x: Int?) -> String {
  // This function uses pattern matching to deconstruct optionals
  switch x {
  case .none: 
    return "No value"
  case .some(let y): 
    return "The value is: \(y)"
  }
}

print(compute(42)) // The value is: 42
print(compute(nil)) // No value
func compute(_ x: Int?) -> String {
  // This function asserts that x has a value, forcefully unwraps x
  // and CRASHES if nil is encountered!
  return "The value is: \(x!)"
}

print(compute(42)) // The value is: 42
print(compute(nil)) // Crash!

Rust

Rust allows using either pattern matching or optional binding to deconstruct the Option type:

fn main() {
    // This function uses pattern matching to deconstruct optionals
    fn compute(x: Option<i32>) -> String {
        match x {
            Some(a) => format!("The value is: {}", a),
            None    => format!("No value")
        }
    }

    println!("{}", compute(Some(42))); // The value is: 42
    println!("{}", compute(None)); // No value
}
fn main() {
    // This function uses optional binding to deconstruct optionals
    fn compute(x: Option<i32>) -> String {
        if let Some(a) = x {
            format!("The value is: {}", a)
        } else {
            format!("No value")
        }
    }

    println!("{}", compute(Some(42))); // The value is: 42
    println!("{}", compute(None)); // No value
}

See also

References

  1. ^ Martin Odersky; Lex Spoon; Bill Venners (2008). Programming in Scala. Artima Inc. pp. 282–284. ISBN 978-0-9815316-0-1. Retrieved 6 September 2011.